1. Field of the Invention
The present invention relates to a waveform generation apparatus and a waveform generation program that applies a different waveform to an inputted waveform by taking advantage of attractors used in chaos theory, and thereby generating a new waveform accompanied by resonation and attenuation.
2. Description of the Related Art
Conventionally, when creating music, a musician must first consider how to leave listeners with a strong impression of an image formed in the musician's mind for each song. The process of creating music is largely divided into a “composition” process for optimizing melodies and chords, and a “tone determination” process for optimizing tones used to play the composed melodies and chords. In the “tone determination” process, the musician generally finds a tone that fits an image he wishes to express, and uses it as is. The selected tone has a particularly important role in leaving an impression of the musician's music on listeners.
When performing “tone determination”, the musician often extracts “sound impression” which is a feature of sound, or in other words, extracts “sound feature that leaves an impression on people”, and actively uses this feature. However, the extraction of “sound impression” has not been established as a common method and is performed based mostly on experience and sensitivity. Therefore, unless the musician is very experienced, this extraction is difficult.
When the musician therefore spends time and effort to extract “sound impression” matching what he is imagining and finds a tone matching this “sound impression”, the musician frequently reuses the tone in other songs “composed” later, after using it in a single “composed” song. This is because the discovered “sound impression” is very appealing and valuable to the musician, and finding a replacement tone having a similar “sound impression” is extremely difficult. However, repeatedly reusing the same tone may leave listeners with the negative impression that the musician is simply repeatedly reusing sounds of the same tone and lacks creativity. In addition, the originality of each song is lost, and a crucial problem arises in that listeners lose interest in the musician.
In recent years, it has become known that when a method called Takens' plot, which is considered to be similar to information processing performed in a human brain, is used to generate an attractor from a certain sound, an attractor indicating “sound impression” is generated. The reason for this is becoming clear through the study of the mechanism of the human brain.
First, the human brain receives external stimulus as information, and after perceiving what the stimulus is (extracts the features thereof), stores the information. This cognition is thought to be performed not only based on inputted information, but also by referencing information stored by stimuli received in the past. For example, a scene in a movie that overlaps with a personal past experience sometimes evokes strong emotions. This is because the brain references memories of experiences stored in the past when it perceives the scene from the movie, and perceives the scene as a strong stimulus if an experience having the same features are found in the memory. The same applies to when a person hears a sound that he has heard somewhere in the past and feels familiarity with the sound.
In the method by which the brain performs cognition, the brain does not necessarily perceive by referencing memories of the distant past. The more recent past is also considered to have a significant influence on cognition. In addition, sound which is information related to hearing is also considered to be perceived by more recent past sound being referenced.
From the above, it can be said that the “process of selecting a current waveform by a predetermined plot scale” in Takens' plot is very similar to the process of “simultaneously referencing past information when perceiving current information” performed in the brain. Therefore, to the brain, the process of drawing an attractor from a waveform showing sound by Takens' plot is none other than the process of extracting “sound impression” required to perceive the waveform. In other words, an attractor displayed using Takens' plot visually expresses the characterizing portion of the sound, which is its “sound impression”.
For example, a waveform generator having a following configuration is described in Japanese Patent Application Laid-Open (Kokai) Publication No. 2008-275845.
The waveform generator includes a Takens' plot processing means for actualizing embedding of original waveform data in a two-dimensional phase space having a time axis and a wave height value axis to an n-dimensional phase space (n>2) based on Takens' embedding theorem by performing Takens' plot processing based on plot conditions composed of a predetermined plot scale value t and a resampling time Δt, and generating attractor data in the n-dimensional phase space; an attractor displaying means for displaying on a display screen of a display means an attractor trajectory based on the attractor data generated by the Takens' plot processing means; an attractor altering means for generating a variation attractor by altering the shape of a waveform showing the attractor displayed by the attractor displaying means in response to a user operation; and a waveform transformation processing means for generating waveform data in a two-dimensional phase space by performing inverse transformation processing in the Takens' plot processing on the variation attractor generated by the attractor changing means.
By an attractor waveform obtained by Takens' plot being altered and the altered attractor waveform being returned to waveform data in a two-dimensional phase space in this way, music edited by the user can be generated while maintaining the features of the attractor.
On the other hand, as a method of amplifying and attenuating an inputted waveform, a method is conventionally used in which the amplification rate of an inputted waveform is simply changed to perform amplification and attenuation. However, in this method, there is a problem in that only the volume is changed, and the character (tone) of the sound cannot be changed. Therefore, musical sounds having different attributes or musical sounds including harmony cannot be generated.